Ok, time for another out-there question. :wink:

First, a quote from the Wiki page on Fractals:

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by BenoĆ®t Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."

A fractal often has the following features:

It has a fine structure at arbitrarily small scales.

It is too irregular to be easily described in traditional Euclidean geometric language.

It is self-similar (at least approximately or stochastically).

It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).

It has a simple and recursive definition.

And an example:

The Mandelbrot set is a famous example of a fractal.

A closer view of the Mandelbrot set.

Now, imagine a 3D version of a fractal created by an oscillating disturbance at its centre. The oscillation means that the orientation of the fractal (into its mirror image) changes with a certain frequency and that the speed at which the newly created fractal moves away from its source is governed by the medium of propegation it finds itself in. The shape, size and type of the fractal is determined by the particular shape, size and type of the disturbance. It is possible for the shape of two fractals to be equal in every way except for the orientation being in the opposite direction (i.e. it points outward instead of inward).

My question is: Is it possible for the interaction between these two fractals, equal except for orientation, to exert an attractive force on each other? Would two of the exact same fractals then exert a repulsive force on each other?